On conditional expectations in L &lt;sup&gt;p&lt;/sup&gt; (μ; L &lt;sup&gt;q&lt;/sup&gt; (ν; X))

Lü, Qi; van Neerven, J.M.A.M.

doi:10.1007/s11117-018-0589-y

On conditional expectations in L ^p (μ; L ^q (ν; X))

Title

On conditional expectations in L ^p (μ; L ^q (ν; X))

Author

Lü, Qi (Sichuan University)
van Neerven, J.M.A.M. (TU Delft Analysis)

Date

2019

Abstract

Let (A, A, μ) and (B, B, ν) be probability spaces, let F be a sub-σ-algebra of the product σ-algebra A× B, let X be a Banach space and let 1 < p, q< ∞. We obtain necessary and sufficient conditions in order that the conditional expectation with respect to F defines a bounded linear operator from L ^p (μ; L ^q (ν; X)) onto LFp(μ;Lq(ν;X)), the closed subspace in L ^p (μ; L ^q (ν; X)) of all functions having a strongly F-measurable representative.

Subject

Conditional expectations in L (μ; L (ν; X))
Dual of L (μ; L (ν; X))
Radon–Nikodým property

To reference this document use:

http://resolver.tudelft.nl/uuid:697ab4e2-d335-4e87-8982-a7e061ee3500

DOI

https://doi.org/10.1007/s11117-018-0589-y

ISSN

1385-1292

Source

Positivity: an international journal devoted to the theory and applications of positivity in analysis, 23 (1), 11-19

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